Real Numbers and the Dedekind Cut
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Maximum and minimum
Equations are omitted for technical reasons - download the original pdf
In a finite set there is a number that is the greatest element of the interval, called the maximum and denoted max, and a number that is the least element of the interval, called the minimum and denoted min. These are the end-points of the interval respectively. For example, the maximum of the interval [Equation goes here - download the original to see it.] is 1, and the minimum is –1. In an infinite set there may not be a minimum or maximum that is a member of the set; however, an infinite set may be bound above or below.
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Contents of
Real Numbers and the Dedekind Cut
1 Numbers as solutions to equations
2 The irrationality of root 2
3 The set of all rational numbers is dense
4 The Dedekind cut
5 The set of real numbers as an ordered field
6 The ordered field axioms
7 The sets of rational and real numbers are ordered fields.
8 Axiom of completeness
9 Bounded sets of numbers
10 Maximum and minimum
11 Bounded set
12 Least upper bound
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